Algebra Examples

$\frac{s^{2} - 2 s}{s^{2} + 3 s - 10} \div \frac{s - 5}{s + 5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{s^{2} - 2 s}{s^{2} + 3 s - 10} \cdot \frac{s + 5}{s - 5}$

Step 2

Factor $s$ out of $s^{2} - 2 s$ .

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Step 2.1

Factor $s$ out of $s^{2}$ .

$\frac{s \cdot s - 2 s}{s^{2} + 3 s - 10} \cdot \frac{s + 5}{s - 5}$

Step 2.2

Factor $s$ out of $- 2 s$ .

$\frac{s \cdot s + s \cdot - 2}{s^{2} + 3 s - 10} \cdot \frac{s + 5}{s - 5}$

Step 2.3

Factor $s$ out of $s \cdot s + s \cdot - 2$ .

$\frac{s (s - 2)}{s^{2} + 3 s - 10} \cdot \frac{s + 5}{s - 5}$

Step 3

Factor $s^{2} + 3 s - 10$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 10$ and whose sum is $3$ .

$- 2, 5$

Step 3.2

Write the factored form using these integers.

$\frac{s (s - 2)}{(s - 2) (s + 5)} \cdot \frac{s + 5}{s - 5}$

Step 4

Cancel the common factor of $s + 5$ .

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Step 4.1

Factor $s + 5$ out of $(s - 2) (s + 5)$ .

$\frac{s (s - 2)}{(s + 5) (s - 2)} \cdot \frac{s + 5}{s - 5}$

Step 4.2

Cancel the common factor.

$\frac{s (s - 2)}{(s + 5) (s - 2)} \cdot \frac{s + 5}{s - 5}$

Step 4.3

Rewrite the expression.

$\frac{s (s - 2)}{s - 2} \cdot \frac{1}{s - 5}$

Step 5

Multiply $\frac{s (s - 2)}{s - 2}$ by $\frac{1}{s - 5}$ .

$\frac{s (s - 2)}{(s - 2) (s - 5)}$

Step 6

Cancel the common factor of $s - 2$ .

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Step 6.1

Cancel the common factor.

$\frac{s (s - 2)}{(s - 2) (s - 5)}$

Step 6.2

Rewrite the expression.

$\frac{s}{s - 5}$